A comparison theorem for the iterative method with the preconditioner (I + Smax)

  • Authors:

  • Hisashi Kotakemori;Kyouji Harada;Munenori Morimoto;Hiroshi Niki

  • Affiliations:

  • Department of Mathematical Information Science, Faculty of Informatics, Okayama University of Science, Ridai-cho 1-1, Okayama 700, Japan;Department of Mathematical Information Science, Faculty of Informatics, Okayama University of Science, Ridai-cho 1-1, Okayama 700, Japan;Department of Mathematical Information Science, Faculty of Informatics, Okayama University of Science, Ridai-cho 1-1, Okayama 700, Japan;Department of Mathematical Information Science, Faculty of Informatics, Okayama University of Science, Ridai-cho 1-1, Okayama 700, Japan

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2002

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Abstract

In 1991, Gunawardena et al. (Linear Algebra Appl. 154-156 (1991) 123) have reported the modified Gauss-Seidel method with a preconditioner (I + S). In this article, we propose to use a preconditioner (I + Smax) instead of (I + S). Here, Smax is constructed by only the largest element at each row of the upper triangular part of A. By using the lemma established Neumann and Plemmons (Linear Algebra Appl. 88/89 (1987) 559), we get the comparison theorem for the proposed method. Simple numerical examples are also given.